All of Buffy and Angel was filmed in 16:9 but framed for 4.3. The only difference in filming was the first season and about half of the episodes in season 2 were shot on 16mm.
This was chosen over strictly shooting to 4.3 because it affects things like focus and zoom angles and the like. A good example is the "Spielberg shots" at the end of the credits. Those close-ups on Sarah's face would look different if they were shot strictly to 4:3 or kept at 16:9. Plus, shotting directly to 4:3 for TV at the time usually meant using tape instead of film for cost.
Assuming the episodes were never going to be presented outside of 4:3, the production staff took little care as to what was left on film but out of frame. However, by mid '99 after Clinton really started pushing the "HD Future" thing, networks started making efforts to future-proof their shows. As such, they basically told Whedon to keep the entire shot 'clean' - i.e. keep all the stagehands and equipment and whatnot out of the film exposure completely.
Despite this, Whedon, Contner, etc. approaching shot set-ups, lens choice, lighting, and all that with the assumption the shows would forever be presented in 4:3. So, starting with season four, even though the masters had nice clean 16:9 reels, the intent was they'd be framed down for broadcast. And they were all through Buffy and up the last season of Angel. ("Once More With Feeling" is the only exception. It was shot and presented fully in 16:9.) However, the WB disregarded the "artistry" and broadcast in 16:9 for season five of Angel, anyway. Though it was still in 480p, so it wasn't really HD.
As far as the DVD releases, there were three separate versions released. (Though I think the second was really just a change in packaging.) The first release - which was seasons by season and started while the show was still on the air - kept the 4:3 aspect ration for everywhere except Region 2 which, for whatever reason, left seasons six and seven in 16:9. This made have had something to do with Paramount over WB, but I don't know because Fox was in charge of the home distribution. Then in the last release, which was the full series collection (and added a bunch of extras), added seasons 4 and 5 to 16:9 everywhere except region 1, which kept 4:3 for all seasons. In other words, the big box set remains 4:3 throughout the series in North America. For the whole rest of the world, it changes to 16:9 from season four onwards.
The ridiculous thing about the badness of the remasters is, even if they wanted to have it in 16:9, they could have just upscaled the last four seasons from the 16:9 masters like they did for Gilmore Girls. (WB told ASP the same thing they told Whedon, but she chose to approach filming the same way he did. So GG also presented in 4:3 despite the stock being 16:9.) But they didn't. They cropped them, which makes for some ridiculous framing in some shots. But I digress...
I don't know anything about the Angel home releases. I never bought them or cared enough to look into it.